Quasi-Linear Transfer Function: A New Method for Frequency Domain Analysis of Nonlinear Systems

TL;DR

This paper introduces quasi-linear transfer functions (QLTF), a novel approach based on Volterra series, enabling frequency domain analysis of nonlinear systems by expressing their output behavior through one-dimensional functions similar to linear frequency response functions.

Contribution

The paper presents the concept of QLTF and algorithms to determine output frequency ranges for nonlinear subsystems, advancing nonlinear system analysis methods.

Findings

QLTF characterizes nonlinear output frequency behavior.

Algorithms determine valid output frequency ranges.

Provides new insights into nonlinear system analysis.

Abstract

A new concept, called quasi-linear transfer functions (QLTF), which can be used to characterize the output frequency behaviour of nonlinear systems, is introduced based on the well-known Volterra series representation. By using the new concept of QLTF, it can be proved that the input and output frequency behaviour of a given system can be expressed using a number of one-dimensional functions with a form similar to that of the traditional frequency response function for linear systems. Two algorithms, which can be used to determine the valid range of the associated output frequencies of arbitrary order nonlinear subsystems with both a multitone and general inputs, are provided. The results obtained provide a new important insight into the output frequency characteristics of nonlinear systems and have many potential applications in nonlinear systems analysis and nonlinear structure detection